Question

1. For each of the following scenarios, write down whether they are most likely to follow a Binomial, Poisson, Exponential or Normal probability distribution. Explain your reasoning. [No calculations are required]
2. 1. A supermarket chain has a toll free phone number for customers to register any complaints. Past records indicate that on average the supermarket chain receives 0.3 complaints per minute. To determine the probability that the supermarket chain receives 3 or more complaint calls in a given minute, the correct distribution would be?
   2. A supermarket chain wants to check the accuracy of price labels of products on the shelves compared to the prices actually charged at its registers. Suppose 3% of products are incorrectly priced on the shelves. To determine the probability that a random selection of 40 products would show no errors, the correct distribution would be?
   3. The most popular item in a bakery is a 625g loaf of ‘Continental’ bread. To minimise the chance of underweight loaves, the baker aims for an average weight of 630g with a standard deviation of 4g. To determine the chance a customer could select a loaf that was less than the advertised weight of 625g, the correct distribution would be?

Answer 1

(i) Poisson distribution, because it is used to describe the distribution of rare events. Here, number of complaints received is 0.3 per minute, which indicates that receipt of complaints is a rare event.

(ii) Binomial distribution, because the 'success' probability of the event is given as 3%. We are observing a specified number of successes in the given sample and there are 2 outcomes - incorrectly priced or correctly priced.

(iii) Normal distribution, because the value of the mean and standard deviation of the population is given here. It is used to fit the distribution of many natural phenomena and since many loaves of bread, they are bound to follow this distribution in the long run.